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M119L11to12-page6 - Sampling Rule for Treating Dependent...

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(Lesson 11: Multiplication Rule; 4-4) 4.19 PART D: SAMPLING RULE FOR TREATING DEPENDENT EVENTS AS INDEPENDENT When we conduct polls, we sample without replacement, so that the same person is not contacted twice. Technically, the selections are dependent. Sometimes, to simplify our calculations, we can treat dependent events as independent, and our results will still be reasonably accurate. We can do this when we take relatively small samples from large populations; then, we can practically assume that we are sampling with replacement, and we can ignore the unlikely possibility of the same item (or person) being selected twice.
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Unformatted text preview: Sampling Rule for Treating Dependent Events as Independent Population (Size N ) ( N ≥ 1000 , say) ↓ (even if we draw without replacement) Sample (Size n ) ( n ≤ 0.05 N ) If we are drawing a sample of size n from a population of size N without replacement, then, even though the selections are dependent, we can practically treat them as independent if: • The sample size is no more than 5% of the population size: n ≤ 5% of N ( ) , or n ≤ 0.05 N , and • The population size, N , is large: say, for our class , N ≥ 1000 ....
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